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Leverage analysis for linear mixed models

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  • Juvêncio S. Nobre
  • Julio M. Singer

Abstract

We consider a generalized leverage matrix useful for the identification of influential units and observations in linear mixed models and show how a decomposition of this matrix may be employed to identify high leverage points for both the marginal fitted values and the random effect component of the conditional fitted values. We illustrate the different uses of the two components of the decomposition with a simulated example as well as with a real data set.

Suggested Citation

  • Juvêncio S. Nobre & Julio M. Singer, 2011. "Leverage analysis for linear mixed models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 1063-1072, February.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:5:p:1063-1072
    DOI: 10.1080/02664761003759016
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    References listed on IDEAS

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    1. Jiang, Jiming, 1999. "On unbiasedness of the empirical BLUE and BLUP," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 19-24, January.
    2. Bo‐Cheng Wei & Yue‐Qing Hu & Wing‐Kam Fung, 1998. "Generalized Leverage and its Applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 25-37, March.
    3. Wing‐Kam Fung & Zhong‐Yi Zhu & Bo‐Cheng Wei & Xuming He, 2002. "Influence diagnostics and outlier tests for semiparametric mixed models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 565-579, August.
    4. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2007. "Assessment of local influence in elliptical linear models with longitudinal structure," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4354-4368, May.
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    Cited by:

    1. Julio M. Singer & Francisco M.M. Rocha & Juvêncio S. Nobre, 2017. "Graphical Tools for Detecting Departures from Linear Mixed Model Assumptions and Some Remedial Measures," International Statistical Review, International Statistical Institute, vol. 85(2), pages 290-324, August.
    2. Duarte Nubia E. & Giolo Suely R. & Pereira Alexandre C. & de Andrade Mariza & Soler Júlia P., 2014. "Using the theory of added-variable plot for linear mixed models to decompose genetic effects in family data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(3), pages 1-20, June.
    3. Pinho, Luis Gustavo B. & Nobre, Juvêncio S. & Singer, Julio M., 2015. "Cook’s distance for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 126-136.
    4. Barranco-Chamorro, I. & Jiménez-Gamero, M.D. & Mayor-Gallego, J.A. & Moreno-Rebollo, J.L., 2015. "A case-deletion diagnostic for penalized calibration estimators and BLUP under linear mixed models in survey sampling," Computational Statistics & Data Analysis, Elsevier, vol. 87(C), pages 18-33.

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